numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/EIG/dget33.f | 7294B | -rw-r--r-- |
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*> \brief \b DGET33 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGET33( RMAX, LMAX, NINFO, KNT ) * * .. Scalar Arguments .. * INTEGER KNT, LMAX, NINFO * DOUBLE PRECISION RMAX * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGET33 tests DLANV2, a routine for putting 2 by 2 blocks into *> standard form. In other words, it computes a two by two rotation *> [[C,S];[-S,C]] where in *> *> [ C S ][T(1,1) T(1,2)][ C -S ] = [ T11 T12 ] *> [-S C ][T(2,1) T(2,2)][ S C ] [ T21 T22 ] *> *> either *> 1) T21=0 (real eigenvalues), or *> 2) T11=T22 and T21*T12<0 (complex conjugate eigenvalues). *> We also verify that the residual is small. *> \endverbatim * * Arguments: * ========== * *> \param[out] RMAX *> \verbatim *> RMAX is DOUBLE PRECISION *> Value of the largest test ratio. *> \endverbatim *> *> \param[out] LMAX *> \verbatim *> LMAX is INTEGER *> Example number where largest test ratio achieved. *> \endverbatim *> *> \param[out] NINFO *> \verbatim *> NINFO is INTEGER *> Number of examples returned with INFO .NE. 0. *> \endverbatim *> *> \param[out] KNT *> \verbatim *> KNT is INTEGER *> Total number of examples tested. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_eig * * ===================================================================== SUBROUTINE DGET33( RMAX, LMAX, NINFO, KNT ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER KNT, LMAX, NINFO DOUBLE PRECISION RMAX * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) DOUBLE PRECISION TWO, FOUR PARAMETER ( TWO = 2.0D0, FOUR = 4.0D0 ) * .. * .. Local Scalars .. INTEGER I1, I2, I3, I4, IM1, IM2, IM3, IM4, J1, J2, J3 DOUBLE PRECISION BIGNUM, CS, EPS, RES, SMLNUM, SN, SUM, TNRM, $ WI1, WI2, WR1, WR2 * .. * .. Local Arrays .. DOUBLE PRECISION Q( 2, 2 ), T( 2, 2 ), T1( 2, 2 ), T2( 2, 2 ), $ VAL( 4 ), VM( 3 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DLANV2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SIGN * .. * .. Executable Statements .. * * Get machine parameters * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM * * Set up test case parameters * VAL( 1 ) = ONE VAL( 2 ) = ONE + TWO*EPS VAL( 3 ) = TWO VAL( 4 ) = TWO - FOUR*EPS VM( 1 ) = SMLNUM VM( 2 ) = ONE VM( 3 ) = BIGNUM * KNT = 0 NINFO = 0 LMAX = 0 RMAX = ZERO * * Begin test loop * DO 150 I1 = 1, 4 DO 140 I2 = 1, 4 DO 130 I3 = 1, 4 DO 120 I4 = 1, 4 DO 110 IM1 = 1, 3 DO 100 IM2 = 1, 3 DO 90 IM3 = 1, 3 DO 80 IM4 = 1, 3 T( 1, 1 ) = VAL( I1 )*VM( IM1 ) T( 1, 2 ) = VAL( I2 )*VM( IM2 ) T( 2, 1 ) = -VAL( I3 )*VM( IM3 ) T( 2, 2 ) = VAL( I4 )*VM( IM4 ) TNRM = MAX( ABS( T( 1, 1 ) ), $ ABS( T( 1, 2 ) ), ABS( T( 2, 1 ) ), $ ABS( T( 2, 2 ) ) ) T1( 1, 1 ) = T( 1, 1 ) T1( 1, 2 ) = T( 1, 2 ) T1( 2, 1 ) = T( 2, 1 ) T1( 2, 2 ) = T( 2, 2 ) Q( 1, 1 ) = ONE Q( 1, 2 ) = ZERO Q( 2, 1 ) = ZERO Q( 2, 2 ) = ONE * CALL DLANV2( T( 1, 1 ), T( 1, 2 ), $ T( 2, 1 ), T( 2, 2 ), WR1, $ WI1, WR2, WI2, CS, SN ) DO 10 J1 = 1, 2 RES = Q( J1, 1 )*CS + Q( J1, 2 )*SN Q( J1, 2 ) = -Q( J1, 1 )*SN + $ Q( J1, 2 )*CS Q( J1, 1 ) = RES 10 CONTINUE * RES = ZERO RES = RES + ABS( Q( 1, 1 )**2+ $ Q( 1, 2 )**2-ONE ) / EPS RES = RES + ABS( Q( 2, 2 )**2+ $ Q( 2, 1 )**2-ONE ) / EPS RES = RES + ABS( Q( 1, 1 )*Q( 2, 1 )+ $ Q( 1, 2 )*Q( 2, 2 ) ) / EPS DO 40 J1 = 1, 2 DO 30 J2 = 1, 2 T2( J1, J2 ) = ZERO DO 20 J3 = 1, 2 T2( J1, J2 ) = T2( J1, J2 ) + $ T1( J1, J3 )* $ Q( J3, J2 ) 20 CONTINUE 30 CONTINUE 40 CONTINUE DO 70 J1 = 1, 2 DO 60 J2 = 1, 2 SUM = T( J1, J2 ) DO 50 J3 = 1, 2 SUM = SUM - Q( J3, J1 )* $ T2( J3, J2 ) 50 CONTINUE RES = RES + ABS( SUM ) / EPS / TNRM 60 CONTINUE 70 CONTINUE IF( T( 2, 1 ).NE.ZERO .AND. $ ( T( 1, 1 ).NE.T( 2, $ 2 ) .OR. SIGN( ONE, T( 1, $ 2 ) )*SIGN( ONE, T( 2, $ 1 ) ).GT.ZERO ) )RES = RES + ONE / EPS KNT = KNT + 1 IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 80 CONTINUE 90 CONTINUE 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE * RETURN * * End of DGET33 * END